Example evaluation of FOCUS Example Dataset D

+ + + +

This is just a very simple vignette showing how to fit a degradation +model for a parent compound with one transformation product using +mkin. After loading the library we look at the data. We +have observed concentrations in the column named value at +the times specified in column time for the two observed +variables named parent and m1.

+library(mkin, quietly = TRUE)
+print(FOCUS_2006_D)

##      name time  value
+## 1  parent    0  99.46
+## 2  parent    0 102.04
+## 3  parent    1  93.50
+## 4  parent    1  92.50
+## 5  parent    3  63.23
+## 6  parent    3  68.99
+## 7  parent    7  52.32
+## 8  parent    7  55.13
+## 9  parent   14  27.27
+## 10 parent   14  26.64
+## 11 parent   21  11.50
+## 12 parent   21  11.64
+## 13 parent   35   2.85
+## 14 parent   35   2.91
+## 15 parent   50   0.69
+## 16 parent   50   0.63
+## 17 parent   75   0.05
+## 18 parent   75   0.06
+## 19 parent  100     NA
+## 20 parent  100     NA
+## 21 parent  120     NA
+## 22 parent  120     NA
+## 23     m1    0   0.00
+## 24     m1    0   0.00
+## 25     m1    1   4.84
+## 26     m1    1   5.64
+## 27     m1    3  12.91
+## 28     m1    3  12.96
+## 29     m1    7  22.97
+## 30     m1    7  24.47
+## 31     m1   14  41.69
+## 32     m1   14  33.21
+## 33     m1   21  44.37
+## 34     m1   21  46.44
+## 35     m1   35  41.22
+## 36     m1   35  37.95
+## 37     m1   50  41.19
+## 38     m1   50  40.01
+## 39     m1   75  40.09
+## 40     m1   75  33.85
+## 41     m1  100  31.04
+## 42     m1  100  33.13
+## 43     m1  120  25.15
+## 44     m1  120  33.31

Next we specify the degradation model: The parent compound degrades +with simple first-order kinetics (SFO) to one metabolite named m1, which +also degrades with SFO kinetics.

The call to mkinmod returns a degradation model. The differential +equations represented in R code can be found in the character vector +$diffs of the mkinmod object. If a C compiler +(gcc) is installed and functional, the differential equation model will +be compiled from auto-generated C code.

+SFO_SFO <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))

## Temporary DLL for differentials generated and loaded

+print(SFO_SFO$diffs)

##                                                    parent 
+##                          "d_parent = - k_parent * parent" 
+##                                                        m1 
+## "d_m1 = + f_parent_to_m1 * k_parent * parent - k_m1 * m1"

We do the fitting without progress report +(quiet = TRUE).

+fit <- mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE)

## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, quiet = TRUE): Observations with
+## value of zero were removed from the data

A plot of the fit including a residual plot for both observed +variables is obtained using the plot_sep method for +mkinfit objects, which shows separate graphs for all +compounds and their residuals.

+plot_sep(fit, lpos = c("topright", "bottomright"))

Confidence intervals for the parameter estimates are obtained using +the mkinparplot function.

+mkinparplot(fit)

A comprehensive report of the results is obtained using the +summary method for mkinfit objects.

+summary(fit)

## mkin version used for fitting:    1.2.10 
+## R version used for fitting:       4.4.2 
+## Date of fit:     Fri Feb 14 08:59:09 2025 
+## Date of summary: Fri Feb 14 08:59:09 2025 
+## 
+## Equations:
+## d_parent/dt = - k_parent * parent
+## d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+## 
+## Model predictions using solution type analytical 
+## 
+## Fitted using 401 model solutions performed in 0.053 s
+## 
+## Error model: Constant variance 
+## 
+## Error model algorithm: OLS 
+## 
+## Starting values for parameters to be optimised:
+##                   value   type
+## parent_0       100.7500  state
+## k_parent         0.1000 deparm
+## k_m1             0.1001 deparm
+## f_parent_to_m1   0.5000 deparm
+## 
+## Starting values for the transformed parameters actually optimised:
+##                      value lower upper
+## parent_0        100.750000  -Inf   Inf
+## log_k_parent     -2.302585  -Inf   Inf
+## log_k_m1         -2.301586  -Inf   Inf
+## f_parent_qlogis   0.000000  -Inf   Inf
+## 
+## Fixed parameter values:
+##      value  type
+## m1_0     0 state
+## 
+## 
+## Warning(s): 
+## Observations with value of zero were removed from the data
+## 
+## Results:
+## 
+##        AIC      BIC    logLik
+##   204.4486 212.6365 -97.22429
+## 
+## Optimised, transformed parameters with symmetric confidence intervals:
+##                 Estimate Std. Error   Lower    Upper
+## parent_0        99.60000    1.57000 96.4000 102.8000
+## log_k_parent    -2.31600    0.04087 -2.3990  -2.2330
+## log_k_m1        -5.24700    0.13320 -5.5180  -4.9770
+## f_parent_qlogis  0.05792    0.08926 -0.1237   0.2395
+## sigma            3.12600    0.35850  2.3960   3.8550
+## 
+## Parameter correlation:
+##                   parent_0 log_k_parent   log_k_m1 f_parent_qlogis      sigma
+## parent_0         1.000e+00    5.174e-01 -1.688e-01      -5.471e-01 -1.172e-06
+## log_k_parent     5.174e-01    1.000e+00 -3.263e-01      -5.426e-01 -8.479e-07
+## log_k_m1        -1.688e-01   -3.263e-01  1.000e+00       7.478e-01  8.211e-07
+## f_parent_qlogis -5.471e-01   -5.426e-01  7.478e-01       1.000e+00  1.305e-06
+## sigma           -1.172e-06   -8.479e-07  8.211e-07       1.305e-06  1.000e+00
+## 
+## Backtransformed parameters:
+## Confidence intervals for internally transformed parameters are asymmetric.
+## t-test (unrealistically) based on the assumption of normal distribution
+## for estimators of untransformed parameters.
+##                 Estimate t value    Pr(>t)     Lower     Upper
+## parent_0       99.600000  63.430 2.298e-36 96.400000 1.028e+02
+## k_parent        0.098700  24.470 4.955e-23  0.090820 1.073e-01
+## k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
+## f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
+## sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
+## 
+## FOCUS Chi2 error levels in percent:
+##          err.min n.optim df
+## All data   6.398       4 15
+## parent     6.459       2  7
+## m1         4.690       2  8
+## 
+## Resulting formation fractions:
+##                 ff
+## parent_m1   0.5145
+## parent_sink 0.4855
+## 
+## Estimated disappearance times:
+##           DT50   DT90
+## parent   7.023  23.33
+## m1     131.761 437.70
+## 
+## Data:
+##  time variable observed predicted   residual
+##     0   parent    99.46  99.59848 -1.385e-01
+##     0   parent   102.04  99.59848  2.442e+00
+##     1   parent    93.50  90.23787  3.262e+00
+##     1   parent    92.50  90.23787  2.262e+00
+##     3   parent    63.23  74.07319 -1.084e+01
+##     3   parent    68.99  74.07319 -5.083e+00
+##     7   parent    52.32  49.91207  2.408e+00
+##     7   parent    55.13  49.91207  5.218e+00
+##    14   parent    27.27  25.01258  2.257e+00
+##    14   parent    26.64  25.01258  1.627e+00
+##    21   parent    11.50  12.53462 -1.035e+00
+##    21   parent    11.64  12.53462 -8.946e-01
+##    35   parent     2.85   3.14787 -2.979e-01
+##    35   parent     2.91   3.14787 -2.379e-01
+##    50   parent     0.69   0.71624 -2.624e-02
+##    50   parent     0.63   0.71624 -8.624e-02
+##    75   parent     0.05   0.06074 -1.074e-02
+##    75   parent     0.06   0.06074 -7.382e-04
+##     1       m1     4.84   4.80296  3.704e-02
+##     1       m1     5.64   4.80296  8.370e-01
+##     3       m1    12.91  13.02400 -1.140e-01
+##     3       m1    12.96  13.02400 -6.400e-02
+##     7       m1    22.97  25.04476 -2.075e+00
+##     7       m1    24.47  25.04476 -5.748e-01
+##    14       m1    41.69  36.69003  5.000e+00
+##    14       m1    33.21  36.69003 -3.480e+00
+##    21       m1    44.37  41.65310  2.717e+00
+##    21       m1    46.44  41.65310  4.787e+00
+##    35       m1    41.22  43.31313 -2.093e+00
+##    35       m1    37.95  43.31313 -5.363e+00
+##    50       m1    41.19  41.21832 -2.832e-02
+##    50       m1    40.01  41.21832 -1.208e+00
+##    75       m1    40.09  36.44704  3.643e+00
+##    75       m1    33.85  36.44704 -2.597e+00
+##   100       m1    31.04  31.98162 -9.416e-01
+##   100       m1    33.13  31.98162  1.148e+00
+##   120       m1    25.15  28.78984 -3.640e+00
+##   120       m1    33.31  28.78984  4.520e+00

Johannes +Ranke

Last change 31 January 2019 +(rebuilt 2025-02-14)